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NC-smooth algebroid thickenings for families of vector bundles and quiver representations

Part of: Families, fibrations Algebraic geometry: Foundations

Published online by Cambridge University Press:  18 March 2019

Ben Dyer  and
Alexander Polishchuk
Ben Dyer
Affiliation:
The Evergreen State College, Olympia, WA 98505, USA email dyerb@evergreen.edu
Alexander Polishchuk
Affiliation:
University of Oregon, Eugene, OR 97405, USA National Research University Higher School of Economics, Moscow, Russia email apolish@uoregon.edu
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Abstract

In his work on deformation quantization of algebraic varieties Kontsevich introduced the notion of algebroid as a certain generalization of a sheaf of algebras. We construct algebroids which are given locally by NC-smooth thickenings in the sense of Kapranov, over two classes of smooth varieties: the bases of miniversal families of vector bundles on projective curves, and the bases of miniversal families of quiver representations.

Keywords

NC-smooth thickeningNC-nilpotent algebraalgebroidmoduli of vector bundlesquiver representations

MSC classification

Primary: 14A22: Noncommutative algebraic geometry
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 4 , April 2019 , pp. 681 - 710
Copyright
© The Authors 2019 

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